A026243 - OEIS

%I #37 Apr 26 2019 03:11:01

%S 0,3,14,63,324,1955,13698,109599,986408,9864099,108505110,1302061343,

%T 16926797484,236975164803,3554627472074,56874039553215,

%U 966858672404688,17403456103284419,330665665962403998,6613313319248079999,138879579704209680020,3055350753492612960483

%N a(n) = A000522(n) - 2.

%C Number of operations of addition and multiplication needed to evaluate a determinant of order n by cofactor expansion.

%H Alois P. Heinz, <a href="/A026243/b026243.txt">Table of n, a(n) for n = 1..170</a>

%H C. Dubbs and D. Siegel, <a href="http://www.jstor.org/stable/2686317">Computing determinants</a>, College Math. J., 18 (1987), 48-49.

%H A. R. Pargeter, <a href="http://www.jstor.org/stable/3618385">The vanishing coffee morning</a>, Math. Gaz., 76 (1992), 386-387.

%H P. G. Sawtelle, <a href="http://www.jstor.org/stable/2689455">The ubiquitous e</a>, Math. Mag., 49 (1976), 244-245. [_N. J. A. Sloane_, Jan 29 2009]

%F a(n) = n*(a(n-1)+2)-1 for n>1, a(1) = 0. - _Alois P. Heinz_, May 25 2012

%F Conjecture: a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - _R. J. Mathar_, Jun 23 2013 [Confirmed by _Altug Alkan_, May 18 2018]

%F a(n) = floor(e*n!) - 2. - _Bernard Schott_, Apr 21 2019

%e To calculate a determinant of order 3:

%e     |a b c|       |e f|       |d f|       |d e|

%e D = |d e f| = a * |h i| - b * |g i| + c * |g h| =

%e     |g h i|

%e    = a * (e*i - f*h) - b * (d*i - f*g) + c * (d*h - e*g).

%e There are 9 multiplications * and 5 additions (+ or -), so 14 operations and a(3) = 14. - _Bernard Schott_, Apr 21 2019

%p a:= proc(n) a(n):= n*(a(n-1)+2)-1: end: a(1):= 0:

%p seq (a(n), n=1..30);  # _Alois P. Heinz_, May 25 2012

%t Table[E*Gamma[n+1, 1] - 2, {n, 1, 30}] (* _Jean-François Alcover_, May 18 2018 *)

%Y Cf. A000522, A007526. Equals A033312 + A038156.

%Y Cf. A001339.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, based on a message from a correspondent who wishes to remain anonymous, Dec 21 2003